Currently there exists a vast interest in exploring the possibility of increasing traffic flow multifold on a fiber simply by exploiting the orthogonality of the orbital angular momentum (OAM) modes [1]}. However, any such effort must take into account fiber imperfections, like ellipticity, which can cause mode-mixing (crosstalk) and reduce the quality of the signal.
An analytic treatment of the effect of ellipticity on OAM modes was earlier provided [2]}, but it was limited to a low topological charge \(l\) , primarily \(l=1\)  or 2 (\(l\)  is the OAM carried by a single photon in units of the reduced Planck's constant (\(h/(2\pi )\) ); besides, the methodology as presented could not incorporate mode mixing with the neighboring OAM modes differing in topological charges by a unit or more. More recently, several authors have carried out numerical studies of the impact of ellipticity on OAM modes in a variety of fibers: ring fiber [3]}, [4]}, [5]}, multi-ring fiber with trench [6]}, and a graded-index fiber [7]} but the studies are based on computationally-intensive finite-element approximation methods, where it is not always easy to ascertain the inherent behavior of the impact of a perturbation like ellipticity in any detailed manner due to the associated high demands of accuracy.
